
For multi-objective problems, multi-objective GA algorithms, such as [1]}, are ideal candidates for obtaining a Pareto-front of optimal solutions. Within a GA generation, the members of a non-dominated Pareto-front are ranked by a `distance crowding function'. This can be computed in decision-variable space, in function space or a hybrid of the two. The ranking takes place when choosing the test points from an acquisition function for a multi-objective problem because the choice must take into account the diversity of the solution and propagate the Pareto-front.

Because the members of the population are ranked by the GA, we can easily extract a `\(Q\) -batch' of points from each of the acquisition functions without needing to add any `pretend' cost function evaluations or optimizing the acquisition functions again.

Genetic algorithms (GA) can be constrained to work in mixed variable spaces. These variables can be dealt with by using probabilistic mutation rates. The genes are allowed to mutate within their prescribed categories, thereby constraining the proposed test points to the \(\mathcal {W}\)  space.

